Superconductor-Insulator Transition and Fermi-Bose Crossovers

Abstract

The direct transition from an insulator to a superconductor (SC) in Fermi systems is a problem of long-standing interest, which necessarily goes beyond the standard BCS paradigm of superconductivity as a Fermi surface instability. We introduce here a simple, translationally-invariant lattice fermion model that undergoes a SC-insulator transition (SIT) and elucidate its properties using analytical methods and quantum Monte Carlo simulations. We show that there is a fermionic band insulator to bosonic insulator crossover in the insulating phase and a BCS-to-BEC crossover in the SC. The SIT is always found to be from a bosonic insulator to a BEC-like SC, with an energy gap for fermions that remains finite across the SIT. The energy scales that go critical at the SIT are the gap to pair excitations in the insulator and the superfluid stiffness in the SC. In addition to giving insights into important questions about the SIT in solid state systems, our model should be experimentally realizable using ultracold fermions in optical lattices.

article 5 pages with 5 figures, four Appendices with 3 figures; total 9 pages

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Cited by in corpus (20)

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• Direct evidence for Cooper pairing without a spectral gap in a disordered superconductor above $T_C$
• Strain induced superconductor-insulator transition on Lieb lattice
• Critical behaviour in one dimension: unconventional pairing, phase separation, BEC-BCS crossover and magnetic Lifshitz transition
• Andreev reflection spectroscopy in strongly paired superconductors
• Self-consistent-field ensembles of disordered Hamiltonians: Efficient solver and application to superconducting films
• Robust Fermi liquid instabilities in sign problem-free models
• Multifractally-enhanced superconductivity in two-dimensional systems with spin-orbit coupling
• Disorder in interacting quasi-one-dimensional systems: flat and dispersive bands
• Charge excitations across a superconductor-insulator transition
• Ultrasonic attenuation in a pseudogapped superconductor
• Dynamic properties of superconductors: Anderson-Bogoliubov mode and Berry phase in BCS and BEC regimes
• Spatial BCS-BEC crossover in superconducting p-n junctions
• Dynamical effects on superconductivity in BCS-BEC crossover
• Quasiparticle Screening near a Bosonic Superconductor-Insulator Transition Revealed by Magnetic Impurity Doping
• Temperature-driven BCS-BEC crossover in a coupled boson-fermion system
• Paraconductivity of pseudogapped superconductors
• Spin gauge theory, duality and fermion pairing
• In-gap states of magnetic impurity in quantum spin Hall insulator proximitized to a superconductor
• SNS Junctions along the BCS-BEC Crossover